E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Cockatrice (3 syl.).
A monster with the wings of a fowl, tail of a dragon
and head of a cock. So called because it was said to be produced from a cocks egg hatched by a serpent. According to legend, the very look of this monster would cause instant death. In consequence of the crest with which the head is crowned, the creature is called a basilisk, from the Greek, basiliskos (a little king). Isaiah says, The weaned child shall put his hand on the cockatrice den (xi. 8), to signify that the most noxious animal should not hurt the most feeble of Gods creatures.
Figuratively, it means an insidious, treacherous person bent on mischief.
They will kill one another by the look, like cockatrices.Shakespeare: Twelfth Night, iii. 4.